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PS-standard deviation

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Director
Joined: 04 Jan 2008
Posts: 893

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29 Mar 2009, 02:09
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500 records have a distribution that is symmetric about the mean 10. If 68 percent of the distribution lies within one standard deviation of the mean, and the deviation is 2, then at least how many of the records are less than 12?

(A) 160
(B) 320
(C) 340
(D) 420
(E) 460

pls explain
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GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

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29 Mar 2009, 08:21
nitya34 wrote:
500 records have a distribution that is symmetric about the mean 10. If 68 percent of the distribution lies within one standard deviation of the mean, and the deviation is 2, then at least how many of the records are less than 12?

(A) 160
(B) 320
(C) 340
(D) 420
(E) 460

pls explain

If the distribution is symmetric, the number of values below the mean is equal to the number above the mean. If none of the values equal the mean exactly (a technicality we don't need to worry about), we have 250 'below average' records, i.e. with values less than 10. We also know that 68% lie within one standard deviation - 34% of these will be below average, 34% above, because the distribution is symmetric. So from 10 to 12, we have 34% of our values, and below 10 we have another 50%, meaning 84% will have values less than 12. 84% of 500 is 420.
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Manager
Joined: 19 Aug 2006
Posts: 238

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29 Mar 2009, 08:46
nitya34 wrote:
500 records have a distribution that is symmetric about the mean 10. If 68 percent of the distribution lies within one standard deviation of the mean, and the deviation is 2, then at least how many of the records are less than 12?

(A) 160
(B) 320
(C) 340
(D) 420
(E) 460

pls explain

I choose D.

0.68*500=340 are situated within the 8...12 segment of the distribution.
500-340=160 are situated outside the 8...12 segment, or, since it's a normal distribution, 160/2=80 are situated on either side of it outside the 8...12 segment.
Since we need the 0....12 segment, 80+340=420 are situated to the left of 12.
Hope my explanation makes sense.
Director
Joined: 04 Jan 2008
Posts: 893

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29 Mar 2009, 09:30
Thanks @both of you.
Thats the answer and great explanations also!!
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Director
Joined: 01 Apr 2008
Posts: 872
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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29 Mar 2009, 11:18
Great explanation guys..do we have any more problems dealing with standard deviation like this? I saw this for the first time.
Director
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29 Mar 2009, 11:25
On demand I am posting a DS Q

easy one

A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1). The average number of eggs for the 10 nests was 4.
(2). Each of the 10 nests contained the same number of eggs.

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Manager
Joined: 19 Aug 2006
Posts: 238

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29 Mar 2009, 13:10
nitya34 wrote:
On demand I am posting a DS Q

easy one

A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1). The average number of eggs for the 10 nests was 4.
(2). Each of the 10 nests contained the same number of eggs.

It's C.
Director
Joined: 04 Jan 2008
Posts: 893

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30 Mar 2009, 10:53
hey
I never expect you to do silly mistake
why you need cond (1) for C?pls check
I think B will suffice alone as SD becomes Zero
hence OA-B

peraspera wrote:
nitya34 wrote:
On demand I am posting a DS Q

easy one

A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1). The average number of eggs for the 10 nests was 4.
(2). Each of the 10 nests contained the same number of eggs.

It's C.

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Director
Joined: 01 Apr 2008
Posts: 872
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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30 Mar 2009, 20:37
True it should be B:)
nitya34 wrote:
hey
I never expect you to do silly mistake
why you need cond (1) for C?pls check
I think B will suffice alone as SD becomes Zero
hence OA-B

peraspera wrote:
nitya34 wrote:
On demand I am posting a DS Q

easy one

A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1). The average number of eggs for the 10 nests was 4.
(2). Each of the 10 nests contained the same number of eggs.

It's C.
Manager
Joined: 19 Aug 2006
Posts: 238

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31 Mar 2009, 17:21
But of course it's B. It is an easy one, indeed. Sometimes you rush through things, and that's where careless mistakes lurk.
I'm learning with the rest of you (them).
Re: PS-standard deviation   [#permalink] 31 Mar 2009, 17:21
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